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3 years ago

What is the average rate of change from x = −2 to x = 0?

Mathematics

1 answer:

astraxan [27]3 years ago

7 0

The rate of change is +2 or 2 over 1 or 2/1

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There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

2 years ago

O=6+x-24<br> Slope intercept form

lara [203]

Answer:

slope is undefined

Step-by-step explanation:

8 0

3 years ago

Rachel just purchased a homeowners insurance policy for her new home that costs $0.43 per $100. Her home is worth $387,500. What

natita [175]

Answer:

The answer is A.

Do you need an explanation?

387,500 /100 = 3,875

3,875 * 0.43 = 1,666.25

I multiplied, because, if you divide with a decimal, the number increases, instead of decreasing... hope this helps!

8 0

3 years ago

Help please

Novosadov [1.4K]

$General\ equation\ for\ line\ in\ slope\ intercept\ form:\\\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (-7,5)\ (-4,1)\ into\ equation\\\\ 
\left \{ {{5=-7a+b}\ \ \ \ \atop {1=-4a+b\ |*-1}} \right.\\\\ \left \{ {{5=-7a+b}\ \ \ \ \atop {-1=4a-b}} \right.\\\\
+----\\\\Addition\ method\\\\
4=-3a\ \ |:(-3)\\\\
a=-\frac{4}{3}\\\\
b=5+7a=5+7*(-\frac{4}{3})=5-\frac{28}{3}=-4\frac{1}{3}\\\
Answer\ y=-\frac{4}{3}x-4\frac{1}{3}\\\\
Checking\ solution:\\
y-5=-\frac{4}{3}(x+7)
$ $y-5=-\frac{4}{3}x-\frac{28}{3}\\\\
y=-\frac{4}{3}x-\frac{28}{3}+5\\\\
y=-\frac{4}{3}x-4\frac{1}{3}\\\\Answer:B \ and\ D.$

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3 years ago

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A Blue Whale can

V125BC [204]

Answer:

4000

Step-by-step explanation:

6 0

2 years ago

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